Stability of braneworlds with non-minimally coupled multi-scalar fields

Linear stability of braneworld models constructed with multi-scalar fields is very different from that of single-scalar field models. It is well known that both the tensor and scalar perturbation equations of the later can always be written as a supersymmetric Schr\"{o}dinger equation, so it can be shown that the perturbations are stable at linear level. However, in general it is not true for multi-scalar field models and especially there is no effective method to deal with the stability problem of the scalar perturbations for braneworld models constructed with non-minimally coupled multi-scalar fields. In this paper we present a method to investigate the stability of such braneworld models. It is easy to find that the tensor perturbations are stable. For the stability problem of the scalar perturbations, we present a systematic covariant approach. The covariant quadratic order action and the corresponding first-order perturbed equations are derived. By introducing the orthonormal bases in field space and making the Kaluza-Klein decomposition, we show that the Kaluza-Klein modes of the scalar perturbations satisfy a set of coupled Schr\"{o}dinger-like equations, with which the stability of the scalar perturbations and localization of the scalar zero modes can be analyzed according to nodal theorem. The result depends on the explicit models. For superpotential derived barane models, the scalar perturbations are stable, but there exist normalizable scalar zero modes, which will result in unaccepted fifth force on the brane. We also use this method to analyze the $f(R)$ braneworld model with an explicit solution and find that the scalar perturbations are stable and the scalar zero modes can not be localized on the brane, which ensure that there is no extra long-range force and the Newtonian potential on the brane can be recovered.Comment: 13 pages, 3 figure

Gravitational resonances on f(R)f(R)-brane

In this paper, we investigate various $f(R)$-brane models and compare their gravitational resonance structures with the corresponding general relativity (GR)-branes. {Starting from some known GR-brane solutions}, we derive thick $f(R)$-brane solutions such that the metric, scalar field, and scalar potential coincide with those of the corresponding GR-branes. {We find that for branes generated by a single or several canonical scalar fields, there is no obvious distinction between the GR-branes and corresponding $f(R)$-branes in terms of gravitational resonance structure.} Then we discuss the branes generated by K-fields. In this case, there could exist huge differences between GR-branes and $f(R)$-branes.Comment: 17 pages, 14 figures, published versio

Born-Infeld Black Holes in 4D Einstein-Gauss-Bonnet Gravity

A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by D. Glavan and C. Lin [Phys. Rev. Lett. 124, 081301 (2020)], which is intended to bypass the Lovelock's theorem and to yield a non-trivial contribution to the four-dimensional gravitational dynamics. However, the validity and consistency of this theory has been called into question recently. We study a static and spherically symmetric black hole charged by a Born-Infeld electric field in the novel four-dimensional Einstein-Gauss-Bonnet gravity. It is found that the black hole solution still suffers the singularity problem, since particles incident from infinity can reach the singularity. It is also demonstrated that the Born-Infeld charged black hole may be superior to the Maxwell charged black hole to be a charged extension of the Schwarzschild-AdS-like black hole in this new gravitational theory. Some basic thermodynamics of the black hole solution is also analyzed. Besides, we regain the black hole solution in the regularized four-dimensional Einstein-Gauss-Bonnet gravity proposed by H. L\"u and Y. Pang [arXiv:2003.11552].Comment: 13 pages and 18 figures, published versio

Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime

Most no-hair theorems involve the assumption that the scalar field is independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the existence of time-dependent scalar hair outside a stationary black hole in general relativity was ruled out. We generalize this work to modified gravities and non-minimally coupled scalar field with an additional assumption that the spacetime is axisymmetric. It is shown that in higher-order gravity such as metric $f(R)$ gravity the time-dependent scalar hair doesn't exist. While in Palatini $f(R)$ gravity and non-minimally coupled case the time-dependent scalar hair may exist.Comment: 6 pages, no figure

Full linear perturbations and localization of gravity on f(R,T)f(R,T) brane

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.Comment: v3: 8 pages, 2 figures, improved version with minor corrections, accepted by EPJ

Cancer-cell microsurgery using nonlinear optical endomicroscopy

Near-infrared laser-based microsurgery is promising for noninvasive cancer treatment. To make it a safe technique, a therapeutic process should be controllable and energy efficient, which requires the cancer cells to be identifiable and observable. In this work, for the first time we use a miniaturized nonlinear optical endomicroscope to achieve microtreatment of cancer cells labeled with gold nanorods. Due to the high two-photon-excited photoluminescence of gold nanorods, HeLa cells inside a tissue phantom up to 250 &mu;m deep can be imaged by the nonlinear optical endomicroscope. This facilitates microsurgery of selected cancer cells by inducing instant damage through the necrosis process, or by stopping cell proliferation through the apoptosis process. The results indicate that a combination of nonlinear endomicroscopy with gold nanoparticles is potentially viable for minimally invasive cancer treatment.<br /

A braneworld model in a massive gravity

A Randall-Sundrum-like braneworld scenario is constructed in a 5D extension of the Lorentz-violating massive gravity. The gauge hierarchy problem is solved in current model. The linear perturbations are calculated, and it is found that the tensor and vector perturbations are robust and free from the ghost and tachyonic instabilities, however, the scalar perturbation is a ghost filed. After Kaluza-Klein reduction, all the tensor, vector and scalar modes are massive and possess the mass splitting of order of TeV in their respective mass spectra. The massive ground states of tensor and scalar modes propagate only along the brane, however, the vector ground state is absent in the mass spectrum. By introducing the Goldberger-Wise mechanism to stabilize the extra dimension, the 4D effective theory on the brane includes a nearly massless graviton plus three towers of very massive spin-2, spin-1 and ghost spin-0 particles.Comment: 24 pages, 2 figures, with some errors correcte

Detecting Extra Dimension By the Experiment of the Quantum Gravity Induced Entanglement of Masses

It is believed that gravity may be regarded as a quantum coherent mediator. In this work we propose a plan using the Quantum Gravity Induced Entanglement of Masses (QGEM) experiment to test the extra dimension. The experiment involves two freely falling test masses passing though a Stern-Gerlach-like device. We study the entanglement witness of them in the framework of Randall-Sundrum II model (RS-II). It turns out that the system would reach entangled more rapidly in the presence of extra dimension. In particular, this is more significant for large radius of extra dimension